We define skew matrix gamma ring and describe the constitution of Jordan left centralizers derivations on a -ring. also show properties these concepts.

In this letter, a rigorous solution of the chaotic Lozi mapping is given for some regions of the bifurcation parameters. The relevance of this result is that while chaos has been proved for the Lozi mapping, there has not previously been discussion of the possibility of finding a rigorous formula for this solution. This important result is obtained using the Jordan normal form defined for matri...

Let Mn be the set of n × n complex matrices, and for every A ∈ Mn, let Sp(A) denote the spectrum of A. For various types of products A1 ∗ · · · ∗ Ak on Mn, it is shown that a mapping φ : Mn → Mn satisfying Sp(A1 ∗ · · · ∗ Ak) = Sp(φ(A1) ∗ · · · ∗ φ(Ak)) for all A1, . . . , Ak ∈ Mn has the form X → ξS−1XS or A → ξS−1XtS for some invertible S ∈ Mn and scalar ξ. The result covers the special cases...

We study the ground-state properties of hard-core bosons trapped by arbitrary confining potentials on one-dimensional optical lattices. A recently developed exact approach based on the Jordan-Wigner transformation is used. We analyze the large distance behavior of the one-particle density matrix, the momentum distribution function, and the lowest natural orbitals. In addition, the low-density l...

In this paper, we give a characterization of strongly Jordan zero-product preserving maps on normed algebras as a generalization of  Jordan zero-product preserving maps. In this direction, we give some illustrative examples to show that the notions of strongly zero-product preserving maps and strongly Jordan zero-product preserving maps are completely different. Also, we prove that the direct p...